The application of iterative reconstruction algorithms to emission tomography, in particular the expectation-maximum (EM) algorithm for maximum likelihood (ML) reconstruction, has been widely studied although not widely implemented for routine reconstruction of PET data. Efforts to date have focused ont he fundamental issues related to the ML algorithm (e.g., stopping criteria, constraints to improve convergence, image artifacts). In an attempt to obtain quantitative two-dimensional (2-D) images with the ML algorithm, we studied methods of inclusion of the corrections for physical factors associated with PET data, namely, radial resolution nonuniformity, detector normalization, scatter, attenuation, and random coincidences. We have demonstrated that the ML algorithm can produce quantitatively accurate 2-D images. The next step is to extend the algorithm, with all corrections, to three-dimensional (3-D) PET data. NIH is one of the few institutions with the necessary computing power to carry out a full 3-D ML reconstruction. Even with the massively parallel computer used for the 2-D algorithm, however, the 3-D problem becomes unwieldy, in terms of the time, memory, and file sizes required. Implementation of the 3-D ML algorithm will require care in order to take advantage of time and size reduction techniques. Once the algorithm has been implemented and tested, it will be compared with analytic methods of 3-D reconstruction of PET data, both "exact" and approximate, to assess the noise and bias characteristics of images generated with the different algorithms. The goal of this study is to determine the circumstances where this computationally-intensive algorithm may be superior to a faster, but potentially biased, analytic approach and to investigate modifications to the ML algorithm which will improve the speed of reconstruction while retaining the advantages of the algorithm.